On One Convolution Equation in the Theory of Filtration of Random Processes
We study the problems of analytic theory and the numerical-analytic solution of the integral convolution equation of the second kind arrayccε^2f(x)+0rK(x-t)f(t)dt=g(x),& x[0,r)array, where arrayccccε >0,& r∞, & KL_1(-∞, ∞ ),& K(x)=abe^-|x|sdσ (s)0.array The factorization approach is used and developed. The key role in this approach is played by the V. Ambartsumyan nonlinear equation., number=8, journal=Ukrains’kyi Matematychnyi Zhurnal, author=Barsegyan, A. G. and Engibaryan, N. B., year=2014, month=Aug., pages=1092–1105